[{key:"search",phaseStatus:{search:"Finish",write:"Ongoing"}},{key:"abc",phaseStatus:{abc:"start",write:"Ongoing"}},{key:"def",phaseStatus:{def:"Finished",write:"done"}}]

db.collection.aggregate([{$addFields:{phaseStatus:{$arrayElemAt:[{$filter:{input:{$objectToArray:"$phaseStatus"},cond:{$eq:["$$this.k","$key"]}}},0]}}},{$addFields:{phaseStatus:"$phaseStatus.v"}},{$match:{phaseStatus:"Finish"}}])